Method of creating an electro-mechanical energy conversion device

ABSTRACT

There are provided methods for creating energy conversion devices based on the giant flexoelectric effect in non-calamitic liquid crystals. By preparing a substance comprising at least one type of non-calamitic liquid crystal molecules and stabilizing the substance to form a mechanically flexible material, flexible conductive electrodes may be applied to the material to create an electro-mechanical energy conversion device which relies on the giant flexoelectric effect to produce electrical and/or mechanical energy that is usable in such applications as, for example, power sources, energy dissipation, sensors/transducers, and actuators.

GOVERNMENT SUPPORT

The U.S. Government has a paid-up license in this invention and theright in limited circumstances to require the patent owner to licenseothers on reasonable terms as provided for by the terms of grant no.DMR-0606160 awarded by the National Science Foundation (NSF), andcontract no. N00014-07-1-0440 awarded by the U.S. Navy/Office of NavalResearch.

TECHNICAL FIELD

Certain embodiments of the present invention relate toelectro-mechanical energy conversion devices and methods. Moreparticularly, certain embodiments of the present invention relate todevices and methods for converting mechanical energy to electricalenergy, and electrical energy to mechanical energy based on the giantflexoelectric effect observed in certain non-calamitic liquid crystalmolecules.

BACKGROUND

Interconversion between different forms of energy is a crucialcapability in a diverse range of technologies from interplanetary probesto nano-fabricated micro-electronic mechanical systems (MEMS) andeverything in between. Flexoelectricity is a linear coupling betweenorientational deformation (caused by, for example, mechanical flexure)and electric polarization. Flexoelectricity is a unique property oforientationally ordered materials, of which nematic liquid crystals(NLCs) are the best known example. The original flexoelectric effect, orcoupling between electric polarization and elastic flexure in NLCs wasfirst predicted almost 40 years ago. For common calamitic (rod-shaped)liquid crystal molecules (the type of compound ubiquitous in liquidcrystal display applications), the flexoelectric effect is very smalland effectively unusable for many applications of, for example,electro-mechanical energy conversion.

To date, flexoelectric coefficients, which characterize theflexoelectric effect, have mainly been measured using indirect methodssuch as analyzing optical effects produced by electric field induceddirector distortions. Usually, hybrid aligned cells are used, whereeither the sum or difference (depending on the cell geometry) of thecoefficients may be obtained. Such methods often require knowledge ofvarious material parameters such as birefringence, dielectric andelastic constants, and anchoring energies which, ideally, should beindependently measured. Published data on flexoelectric coefficientsshould be handled, however, with some care as various authors haveobtained different values from the same experimental data sets usingdifferent evaluation techniques. This is perhaps not surprising givenhow small the coefficients are for calamitic NLCs.

Further limitations and disadvantages of conventional, traditional, andproposed approaches will become apparent to one of skill in the art,through comparison of such systems and methods with the presentinvention as set forth in the remainder of the present application withreference to the drawings.

BRIEF SUMMARY

An embodiment of the present invention comprises a method of creating anelectro-mechanical energy conversion device. The method includespreparing a substance comprising at least one type of non-calamiticliquid crystal molecules and stabilizing the prepared substance to forma mechanically flexible material. The method further includes applyingflexible conductive electrodes to the material.

Another embodiment of the present invention comprises anelectro-mechanical energy conversion device. The device includes astabilized substance comprising at least one type of non-calamiticliquid crystal molecules forming a mechanically flexible material, andat least two conductive electrodes applied to the material.

A further embodiment of the present invention comprises a method ofdetermining a flexoelectric effect in a liquid crystal material. Themethod includes periodically flexing a stabilized layer of liquidcrystal material interposed between non-rigid electrically conductingsurfaces and measuring an induced electric current flowing between theconducting surfaces.

Another embodiment of the present invention comprises a system fordetermining a flexoelectric effect in a liquid crystal material. Thesystem includes a test chamber having a fixed base and moveable sidewalls. The system also includes a driving mechanism capable of providingperiodic motion and being mechanically coupled to the moveable sidewalls. The system further includes an amplifier electrically coupled tothe driving mechanism to electrically drive the driving mechanism. Thesystem also includes a signal generator electrically coupled to theamplifier to provide a signal of at least one audio frequency to theamplifier. The system further includes a current sensor for measuring anelectric current induced in a liquid crystal material mechanicallycoupled to the moveable side walls of the test chamber.

A further embodiment of the present invention comprises a method ofcreating an electro-mechanical energy conversion device. The methodincludes preparing a substance comprising at least one type ofnon-calamitic liquid crystal molecules capable of exhibiting a giantflexoelectric effect. The method further includes stabilizing theprepared substance to form a mechanically flexible material and applyingrigid conductive electrodes to the material.

Another embodiment of the present invention comprises anelectro-mechanical energy conversion device. The device includes astabilized substance comprising at least one type of non-calamiticliquid crystal molecules forming a mechanically flexible materialcapable of exhibiting a giant flexoelectric effect, and at least tworigid conductive electrodes applied to the material.

Devices employing the giant flexoelectric effect may be light weight,low cost, have dynamic shape conformability, allow for flexiblepackaging, provide larger areal coverage, have a low profile, and/or behuman-person compatible.

These and other advantages and novel features of the present invention,as well as details of illustrated embodiments thereof, will be morefully understood from the following description and drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A-1B are schematic illustrations of an embodiment of an energyconversion device and an embodiment of the non-calamitic liquid crystalmolecules used in the device;

FIG. 2 is a flowchart of an embodiment of a method of creating anelectro-mechanical energy conversion device;

FIG. 3A is a chemical diagram of a first embodiment of a non-calamiticnematic liquid crystal molecule exhibiting the giant flexoelectriceffect;

FIG. 3B is a chemical diagram of a second embodiment of a non-calamiticnematic liquid crystal molecule exhibiting the giant flexoelectriceffect;

FIG. 4 is a chemical diagram of an embodiment of two non-calamiticnematic liquid crystal molecules which, when mixed together, exhibit thegiant flexoelectric effect at room temperature;

FIG. 5 is a schematic illustration of the energy conversion device ofFIG. 1 used in a circuit powering application;

FIG. 6 is a schematic illustration of the energy conversion device ofFIG. 1 used in an energy dissipating application;

FIG. 7 is a schematic illustration of the energy conversion device ofFIG. 1 used in a sensing/transducing application;

FIG. 8 is a schematic illustration of the energy conversion device ofFIG. 1 used in an actuating application;

FIG. 9A is a chemical illustration of the non-calamitic nematic liquidcrystal molecule of FIG. 3A along with a schematic representation of itssimplified geometrical model;

FIG. 9B is a schematic illustration of a first embodiment of a systemfor determining a flexoelectric effect in a liquid crystal material;

FIG. 10A is a schematic illustration of an embodiment of a model of thesample cell geometry of a nematic liquid crystal material;

FIG. 10B is a schematic illustration of an embodiment of the nematicliquid crystal material of FIG. 10A during deformation using the systemof FIG. 9B;

FIG. 11 is a schematic illustration of a second embodiment of a systemfor determining a flexoelectric effect in a liquid crystal material;

FIG. 12 is a flowchart of an embodiment of a method for determining aflexoelectric effect in a liquid crystal material using the system ofFIG. 9B or the system of FIG. 11; and

FIGS. 13A-13B are schematic illustrations of an embodiment of an energyconversion device having interdigitated electrodes.

DETAILED DESCRIPTION

FIGS. 1A-1B are schematic illustrations of an embodiment of an energyconversion device 100 and an embodiment of the non-calamitic liquidcrystal molecules 110 used in the device 100, respectively. As usedherein, the term non-calamitic refers to liquid crystal molecules thatare not substantially rod-shaped. Such non-calamitic molecules mayinclude non-calamitic nematic (i.e., the liquid crystal phase isnematic) liquid crystal molecules such as, for example, bent-corenematic liquid crystal (NLC) molecules (as shown in FIG. 1B) orpear-shaped nematic liquid crystal molecules, for example. Other typesof non-calamitic liquid crystal molecules, which are not nematic andwhich exhibit the giant flexoelectric effect, may be possible as well.

One or more types of non-calamitic liquid crystal molecules 110 may bemixed together and used in the device 100. That is, at least onenon-calamitic material is used in a mixture. For example, non-calamiticmolecules may be mixed with calamitic molecules. Certain types ofnon-calamitic liquid crystal molecules may have one type of functionalgroup and other types may have another type of functional group.Functional groups (or moieties) are specific groups of atoms withinmolecules that are responsible for the characteristic chemical reactionsof those molecules such as, for example, covalent bonding or hydrogenbonding.

Certain, non-calamitic liquid crystal molecules have been discovered toexhibit a “giant flexoelectric effect”. That is, certain non-calamiticliquid crystal molecules have been discovered to exhibit a flexoelectriceffect at least two orders of magnitude greater than that exhibited bytraditional calamitic (substantially rod-shaped) liquid crystalmolecules, making energy conversion devices using such non-calamiticliquid crystal molecules practical. Other non-calamitic liquid crystalmolecules (other than bent-core or pear-shaped) which exhibit the giantflexoelectric effect are possible as well but may have yet to bediscovered, developed, or characterized for their giant flexoelectricproperties. The magnitude of the giant flexoelectric effect depends onthe quantity of the molecules involved, the quality of the alignment ofthe molecules, and the efficiency of transmission of the flexing forceto the molecules. In general, the flexoelectric effect is considered tobe giant when it is larger than 1 nano-coulomb per meter (nC/m), whichis about 100 times larger than 10 pico-coulombs per meter (pC/m) usuallyfound in calamitic liquid crystal molecules.

The device 100 includes a substance, comprising at least thenon-calamitic liquid crystal molecules 110, which is stabilized to forma mechanically flexible material 120 (i.e., a stabilized substance) andat least two flexible conductive electrodes 130 applied to the flexiblematerial 120. In such a configuration, the device 100 may bemechanically flexed, producing a potential difference between theelectrodes 130. Alternatively, a potential difference may be applied tothe electrodes 130, resulting in a flexing of the device 100. Both thematerial 120 and the electrodes 130 flex together such that theelectrodes 130 do not separate from the material 120.

In a non-stabilized state, the non-calamitic liquid crystal molecules110 are fluidic and are not ideally suitable for energy conversiondevices. In order to exploit the giant flexoelectric properties andcreate a material sufficiently rugged for use, the non-calamitic liquidcrystal molecules 110 are encapsulated or stabilized, using a variety ofpossible techniques, into a polymer matrix. Such stabilizationtechniques are described later herein in further detail. The polymermatrix helps to provide more direct coupling of the external flexingaction to the molecules. The resultant stabilized material may have theconsistency of a soft, rubbery product, such that the material may beeasily mechanically deformed to produce electricity, yet is not a liquidwhich has to be confined to maintain a desired shape.

The electrodes may comprise conductive material and are, for example,deposited onto the flexible material 120. Other methods of applying theflexible electrodes 130 to the flexible material 120 are possible aswell, as may be known in the art, in accordance with other variousembodiments of the present invention. Examples of such conductivematerials include electrically conducting polymers, conductive greese,nano-wire mesh, nano-fibers, and conductive metals.

FIG. 2 is a flowchart of an embodiment of a method 200 of creating anelectro-mechanical energy conversion device 100. In step 210, prepare asubstance comprising at least one type of non-calamitic liquid crystalmolecules 110. In optional step 220, align the non-calamitic liquidcrystal molecules 110. The aligning is done such that a direction ofaverage molecular anisotropy in an undistorted (unflexed) state isuniform across the non-calamitic liquid crystal molecules 110. Aligningmay be performed by applying a surface treatment such as by rubbing,applying a mechanical deformation, or applying external electric and/ormagnetic fields as is known in the art. In step 230, stabilize theprepared substance to form a mechanically flexible material 120. Again,such stabilization techniques are described later herein in furtherdetail. In step 240, apply flexible conductive electrodes 130 to theflexible material 120.

FIG. 3A is a chemical diagram of a first embodiment of a non-calamiticnematic liquid crystal molecule 310 exhibiting the giant flexoelectriceffect. The molecule 310 is known as CLPbis10BB and was the firstnon-calamitic NLC molecule observed to exhibit the giant flexoelectriceffect. Notice the bent-core shape of the molecule 310 in the diagram.Similarly, FIG. 3B is a chemical diagram of a second embodiment of anon-calamitic nematic liquid crystal molecule 320 exhibiting the giantflexoelectric effect. The molecule 320 is the saturated version of themolecule 310 (CLPbis10BB) and has been measured to have a flexoelectriceffect being about 50% greater than that of CLPbis10BB.

FIG. 4 is a chemical diagram of an embodiment of two non-calamiticnematic liquid crystal molecules 410 and 420 which, when mixed togetherduring preparation and then stabilized, exhibit the giant flexoelectriceffect at room temperature. A mixture of about 50%/50% of these twomolecules 410 and 420 exhibit a room temperature nematic liquid crystalphase having an isotropic to nematic (I-N) transition at about 85° C.

The process of stabilizing the non-calamitic liquid crystal molecules110 involves forming a polymer mesh or matrix to encapsulate themolecules (at least to a certain degree). For example, in accordancewith an embodiment of the present invention, the step 230 of stabilizingthe prepared substance includes initiating cross-linking between two ormore functional groups of the non-calamitic liquid crystal molecules toform a polymer matrix of covalent bonds. That is, the polymer mesh isformed by the non-calamitic liquid crystal molecules themselves.Cross-linking may be initiated by, for example, photo-initiation,thermal processing, or catalysis. Not all of the molecules 110 withinthe substance have to be cross-linked. In reality, only a small portion(e.g., 5%) of the molecules 110 within the substance may becross-linked, providing enough stabilization to allow effectiveproduction of the giant flexoelectric effect.

Similarly, for example, in accordance with another embodiment of thepresent invention, the step 230 of stabilizing the prepared substanceincludes initiating cross-linking between two or more functional groupsof the non-calamitic liquid crystal molecules to form a polymer matrixof hydrogen bonds. Again, not all of the molecules 110 within thesubstance have to be cross-linked to provide enough stabilization toallow effective production of the giant flexoelectric effect.

In accordance with other embodiments of the present invention, compoundshaving reactive functional groups (i.e., reactive compounds) may bedissolved into the non-calamitic liquid crystal molecules 110 as part ofthe preparation step 210. Then, in the stabilization step 230,cross-linking is initiated between the reactive functional groups toform a polymer matrix of covalent or hydrogen bonds. The cross-linkingof the compounds encapsulates and, therefore, stabilizes thenon-calamitic liquid crystal molecules 110. Examples of such compoundsinclude vinyls, epoxides, and polymers of perfluorinated benzene rings.

In accordance with alternative embodiments of the present invention,stabilization of the non-calamitic liquid crystal molecules 110 may beaccomplished by capturing the prepared substance between elasticsubstrates or by capturing the prepared substance within apre-established polymer mesh. In such alternative embodiments, thenon-calamitic liquid crystal molecules 10 themselves are not used toform the polymer mesh or matrix.

Furthermore, the basic device 100 may be scaled up to form a layeredlaminate product with multiple pairs of electrodes (e.g., interdigitizedelectrodes) to increase efficiency, in accordance with variousembodiments of the present invention. An example is given later withrespect to FIGS. 13A-13B.

FIG. 5 is a schematic illustration of the energy conversion device 100of FIG. 1 used in a circuit powering application. The electrodes 130 ofthe device 100 are connected to a rechargeable power cell 510 which isused to power a circuit 520. The power cell 510 may be a re-chargeablebattery or some other type of re-chargeable power pack. The circuit 520may be any type of electrical circuit which may be powered by the powercell 510. For example, the circuit 520 may comprise an MP3 player, asmall flashlight, a cell phone, a radio, or any other type of devicehaving a power cell 510 that may be re-charged.

When the device 100 is mechanically flexed (e.g., by a human), apotential difference (voltage) is created at the electrodes 130. Byapplying the potential difference (voltage) to the power cell 510, thepower cell 510 is re-charged over time. The device 100 may be integratedinto, for example, a person's clothing (e.g., a shirt) such that, when aperson moves around in the normal course of daily activity, the device100 is flexed and the power cell 510 is re-charged over time as a resultof the giant flexoelectric effect. The combination of the circuit 520,power cell 510, and the flexoelectric device 100 may be considered aclosed circuit electro-mechanical energy conversion device or system500. Many other applications of the device 500 are possible as well, inaccordance with various embodiments of the present invention.

FIG. 6 is a schematic illustration of the energy conversion device 100of FIG. 1 used in an energy dissipating application. The device 100 iselectrically connected to a simple resistive load 610. When the device100 is flexed, a current is induced in the load and the mechanicalenergy flexing the device 100 is converted to electrical energy which isdissipated by the load 610. By varying the load 610, the amount ofmechanical energy converted may be varied. The energy is dissipated bythe resistive load 610 and is no longer available to do mechanical work.Thus, the device 600 functions as a mechanical energy dissipator whichmay be used in applications such as vibration damping, for example.

The combination of the resistive load 610 and the flexoelectric device100 may be considered a closed circuit electro-mechanical energyconversion device or system 600. For example, if a plurality of thedevices 600 are integrated into clothing, such clothing may be used tohelp keep a person warm as they move around in the course of their dailyactivities since the electrical energy absorbed by the resistive loadmay be given off as thermal energy (heat). Many other applications ofthe device 600 are possible as well, in accordance with variousembodiments of the present invention.

FIG. 7 is a schematic illustration of the energy conversion device 100of FIG. 1 used in a sensing/transducing application. The device 100 iselectrically connected to a sensitive current detector 710 such as agalvanometer. When the device 100 is flexed, even by a small amount, ameasurable current registers in the detector 710 as a result of theflexure. The combination of the current detector 710 and theflexoelectric device 100 may be considered a closed circuitelectro-mechanical energy conversion device or system 700. Therefore,the closed circuit device 700, comprising the detector 710 and theflexoelectric device 100, functions as a sensitive sensor/transducer forthe detection of very small flexures or displacements which causeflexures. Such a device 700 may be used, for example, to monitor smallcritical flexures in implantable medical devices. Many otherapplications of the device 700 are possible as well, in accordance withvarious embodiments of the present invention.

FIG. 8 is a schematic illustration of the energy conversion device 100of FIG. 1 used in an actuating application. In such an embodiment 800,the device 100 acts in a reverse mode. That is, instead of convertingmechanical energy into electrical energy, the reverse occurs. When asource of electrical potential difference (voltage) 810 is appliedacross the flexoelectric device 100, flexure is induced in the device100. Therefore, the device 100 functions as an electrically controlledmechanical actuator. The combination of the voltage source 810 and theflexoelectric device 100 may be considered a closed circuitelectro-mechanical energy conversion device or system 800. Such a device800 may be used, for example, to steer a beam of light if one side ofthe flexoelectric device 100 is made to be reflective to light. Thevoltage source 810 may be a variable or adjustable voltage source, inaccordance with an embodiment of the present invention. Many otherapplications of the device 800 are possible as well, in accordance withvarious embodiments of the present invention.

Further, applications of the flexoelectric device 100 other than energyconversion, energy dissipation, sensing/transducing, and actuating maybe possible as well. Wearable products such as, for example, patches onjoints (knees, fingers, elbows, etc.) or in footwear that generateelectrical energy from mechanical work involved in routine lifeactivities (e.g., walking, running, typing, etc.) are possible with thegiant flexoelectric effect. The patches may be light weight and softand, therefore, would not burden the user. The inverse effect ofconverting electrical energy to mechanical work may be employed inrobotics applications and optical beam steering applications, forexample. Designs that work based on pressure such as, for example,dielectric heel-strike generators are possible as well.

The ability to directly and accurately measure the giant flexoelectriceffect for different types of non-calamitic liquid crystal molecules isimportant for identifying molecules that will be effective forparticular applications. FIG. 9A is a chemical illustration of thenon-calamitic nematic liquid crystal molecule 310 of FIG. 3A along witha schematic representation of its simplified geometrical model 910. Aflexoelectric polarization, {right arrow over (P)}_(f), may arise in anormally apolar NLC when the average direction for orientational orderor director, {right arrow over (n)}, is subjected to splay or benddeformations. The effect is enhanced for molecules which possess apermanent dipole moment and shape anisotropies, for example,non-calamitic NLC molecules such as pear-shaped or banana-shapedmolecules. In such cases, orientationally deformed structures havingnonzero {right arrow over (P)}_(f) have both closer molecule packing andlower free energy than non-polar arrangements. In the continuum limit,{right arrow over (P)}_(f) is proportional to the first order spatialderivatives of {right arrow over (n)}. Higher order derivatives arenegligible when the deformation length scale is small compared to themolecular size. The flexoelectric polarization of a standard uniaxialnematic may then be expressed in terms of two flexoelectric coefficientse₁ and e₃, corresponding to splay and bend deformations, respectively:{right arrow over (P)} _(f) =e ₁ {right arrow over (n)}(div {right arrowover (n)})+e ₃(curl {right arrow over (n)})×{right arrow over (n)}.  (1)

A molecular statistical approach to estimate the flexoelectriccoefficients predicts that the bend flexoelectric constant e₃ of abanana shaped molecule may be related to the kink angle θ_(o) 911 in themolecular core:

$\begin{matrix}{e_{3} = {\frac{\mu_{\bot}K_{33}}{2k_{b}T}{\theta_{o}\left( \frac{b}{a} \right)}^{\frac{2}{3}}N^{\frac{1}{3}}}} & (2)\end{matrix}$

In equation (2), μ_(⊥) 912 is the molecular dipole perpendicular to themolecular long axis; ‘a’ 913 and ‘b’ 914 are the length and width of amolecule, T is the absolute temperature, N is the number density of themolecules, and K₃₃ is the bend elastic constant. This approach assumesthat the molecules fluctuate independently. For rod-shaped molecules,θ_(o)<1°, and the flexoelectric coefficients of such NLCs are estimatedto be 1-10 pC/m, in reasonable agreement with measured values. Fortypical banana-shaped molecules, θ_(o)˜60° and, therefore, it isexpected that such bent core NLC molecules have an e₃ being about 100times larger.

A method for measuring the flexoelectric coefficient is directly basedon the definition of equation (1). An oscillatory bend deformation isinduced by periodically flexing a thin layer of liquid crystal materialcontained between non-rigid conducting surfaces. The induced current isthen measured. An exemplary embodiment of a NLC sample includes 150 μmthick polycarbonate sheets, used as flexible substrates, with indium tinoxide (ITO) conductive coating sputtered onto the inner surfaces. Theinner surfaces have been spin-coated with a polyimide layer which hasbeen rubbed unidirectionally to achieve uniform planar alignment of theLC director. Bent-core NLC samples (CLPbis10BB) being 20 μm thick, havebeen loaded into cells constructed from the substrates.

FIG. 9B is a schematic illustration of a first embodiment of a system900 for determining a flexoelectric effect in a liquid crystal material920. A liquid crystal sample 920 is placed in a test chamber 925 havinga fixed bottom plate or base 930 with two vertically orientedcylindrical posts 931 and 932, and movable side walls 940 havingvertical slots 941 and 942. The liquid crystal sample 920 is confinedbetween flexible electrodes 921 and 922 and is inserted between theslots 941 and 942 and the cylindrical posts 931 and 932 as shown in FIG.9B.

Flexing of the liquid crystal sample 920 is achieved by periodicallytranslating the side walls 940 using a vibrating driving mechanism 950(e.g., an audio speaker or Skotch Yoke) capable of providing periodicmotion and which is mechanically coupled to the moveable side walls 940via a rod 951 or some other coupling means. The driving mechanism 950 isdriven by an amplifier 960 electrically coupled to the driving mechanism950 to electrically drive the driving mechanism 950. A signal generatorand a current sensor, shown as an integrated lock-in amplifier 970 inFIG. 9B, are provided. The signal generator is electrically coupled tothe amplifier 960 to provide a signal of at least one audio frequency tothe amplifier 960, and the current sensor is electrically coupled to theflexible electrodes 921 and 922 to measure an induced current in theliquid crystal sample material 920 mechanically coupled to the moveableside walls 940 of the test chamber 925. During operation of the system900, the walls 940 of the test chamber 925 oscillate and the liquidcrystal sample 920 flexes at the same frequency and amplitude as thedriving mechanism 950. The electrodes 921 and 922 of the liquid crystalsample 920 are connected to the current input of the lock-in amplifier970 (current sensor portion) such that the precision with which theelectric polarization current may be measured using this technique is afew pico-amps (pA).

FIG. 10A is a schematic illustration of an embodiment of a model of thesample cell geometry 1000 of a nematic liquid crystal material 920. Thecell 1000 of total length L_(x)+2D and width L_(y) is initially locatedin the x-y plane 1010 and the mechanical displacement occurs along thedirection of the z-axis 1020. The cell 1000 is symmetric with respect toits center and, therefore, the deformation profile of the substrates isgiven by an even function Z(x). The current induced by the flexoelectricpolarization is

${I = {\frac{\mathbb{d}}{\mathbb{d}t}{\int{\int{P_{f}{\mathbb{d}A}}}}}},$where dA is the surface area element and the integration extends overthe whole active area (X×Y) of the cell 1000. In the planar geometry,only the bend term contributes. Therefore, after integration,

$I = {e_{3}Y{{\frac{\mathbb{d}}{\mathbb{d}t}\left\lbrack {{n_{z}\left( {x = {X/2}} \right)} - {n_{z}\left( {x = {{- X}/2}} \right)}} \right\rbrack}.}}$

In the case of the small deformations considered, n_(z) corresponds tothe tangent of the substrates, that is

${{n_{z}(x)} = \frac{\partial{Z(x)}}{\partial x}},$where Z(x) describes the displacement of the substrates and the sample.FIG. 10B is a schematic illustration of an embodiment of the nematicliquid crystal material 920 of FIG. 10A during deformation using thesystem 900 of FIG. 9B. The mechanical deformation corresponds to theclassical problem of bending an elastic sheet found in standard textsand reveals that Z(x)=Sβ(x), where

$\begin{matrix}{{\beta(x)} = {{\frac{1}{4}\left\lbrack {{3\left( \frac{2x}{L_{x}} \right)^{2}} - \left( \frac{2x}{L_{x}} \right)^{3}} \right\rbrack}.}} & (3)\end{matrix}$

Therefore, taking into account that the direction is fixed at the edgesby the slots 941 and 942, the flexoelectric current becomes

$\begin{matrix}{I = {{e_{3}Y\frac{\mathbb{d}S}{\mathbb{d}t}\frac{\mathbb{d}\beta}{\mathbb{d}x}}|_{{- X}/2}^{X/2}}} \\{= {e_{3}Y\frac{\mathbb{d}S}{\mathbb{d}t}{\frac{6X}{L_{x}^{2}}.}}}\end{matrix}$With periodic flexing (S=S_(o) sin ωt, where S_(o) is the peakdisplacement and ω is the frequency of oscillation), the flexoelectriccoefficient may then be determined in terms of the root-mean-square(rms) induced current I_(rms) as

$\begin{matrix}{{e_{3}} = {\frac{\sqrt{2}I_{rms}}{6X\;\omega\; S_{o}}\frac{L_{x}^{2}}{Y}}} & (4)\end{matrix}$

FIG. 11 is a schematic illustration of a second embodiment of a system1100 for determining a flexoelectric effect in a liquid crystal material920. The system 1100 is similar to the system 900 of FIG. 9B but hasadditional components. In order to achieve smooth and uniform motion,the position of the driving mechanism 950 with respect to the moveableside walls 940 is critical and, therefore, may be adjusted using twoperpendicular micro-positioners 1130 and 1140. The micro-positioners maycomprise micro-electric actuators or micro-fluidic actuators, forexample. In accordance with an embodiment of the present invention, themicro-positioners 1130 and 1140 are controlled by a processing device orcontroller 1150 which may comprise, for example, a personal computer(PC) or a programmable logic controller (PLC).

The amplitude (e.g., peak deformation) and/or frequency of the appliedoscillatory deformation may be measured with 0.2 mm precision by aposition-sensing device 1110 either by, for example, mechanicaldetection or my measuring the intensity of a laser diode through aneutral optical gradient filter fixed to the moving rod connecting thetest chamber 925 to the driving mechanism 950.

The test chamber 925 may be enclosed and may be temperature regulated,in accordance with an embodiment of the present invention. A temperaturecontroller 1120 may be used to regulate the temperature of the testchamber 925 with, for example, a precision of ΔT<1° C. between roomtemperature and 160° C. A temperature sensor 1125 connected with thetemperature controller 1120 indicates to the temperature controller 1120the present temperature inside the test chamber 925, such that thetemperature controller 1120 may regulate the temperature of the testchamber 925 in response to the present temperature. The temperaturecontroller 1120 may include a fan, an air conditioner, a heater, or anycombination thereof. Other temperature controllers are possible as well,in accordance with various embodiments of the present invention.

The processing device 1150 may be used to calculate at least oneflexoelectric coefficient (e.g., e₃) in response to at least one of themeasured induced electric current, the measured peak deformation, andthe frequency of oscillation. The processing device 1150 may comprise ahand-held calculator, where all calculations are performed manually byan operator, or a programmable computer-based device such as a PC, wherecalculations are performed automatically in response to inputs receivedfrom at least one of the lock-in amplifier 970, the micro-positioners1130 and 1140, the position-sensing device 1110, and the temperaturecontroller 1120.

FIG. 12 is a flowchart of an embodiment of a method 1200 for determininga flexoelectric effect in a liquid crystal material using the system 900of FIG. 9B or the system 1100 of FIG. 11. In step 1210, periodicallyflex a stabilized layer of liquid crystal material interposed betweennon-rigid electrically conducting surfaces. In step 1220, measure aninduced electric current flowing between the conducting surfaces. Instep 1230, measure and control an ambient temperature of the liquidcrystal material (this step is optional). In step 1240, measure a peakdisplacement and a frequency of oscillation of the liquid crystalmaterial. In step 1250, calculate a flexoelectric coefficient of theliquid crystal material in response to at least one of the measuredinduced current, the measured peak displacement, and the frequency ofoscillation.

The periodic flexing is a result of inducing an oscillatory benddeformation in the layer of liquid crystal material in response to theperiodic driving mechanism (e.g., a vibrating speaker cone). The ambienttemperature of the liquid crystal material is controlled by controllingthe temperature inside the test chamber 925.

In accordance with other embodiments, the basic device 100 may be rolledup or stacked up with electrodes in parallel circuits, or by usinginterdigitated electrodes to increase efficiency. FIG. 13A shows anexemplary embodiment of a stacked, interdigitated configuration 1300 inan unbent or uncompressed state. FIG. 13B shows the stackedconfiguration 1300 in a bent or compressed state. The configuration 1300includes layers of liquid crystal material or film 1310 in betweenfingers of electrodes 1320 (interdigitized electrodes). In such aconfiguration 1300, the interdigitized electrodes 1320 may be rigid.When the external plates or substrates 1330 are pressed, the liquidcrystal material 1310 is bent or flexed between the electrodes 1320 andexhibits the giant flexoelectric effect, thus creating a non-zerovoltage 1340 at the output of the electrodes 1320. Similarly, if avoltage is applied to the electrodes 1320, the configuration 1300becomes compressed.

In summary, devices and methods for energy conversion based on the giantflexoelectric effect in non-calamitic liquid crystals are disclosed. Bypreparing a substance comprising at least one type of non-calamiticliquid crystal molecules and stabilizing the substance to form amechanically flexible material, flexible conductive electrodes may beapplied to the material to create an electro-mechanical energyconversion device which relies on the giant flexoelectric effect toproduce electrical and/or mechanical energy that is usable in suchapplications as, for example, power sources, energy dissipation,sensors/transducers, and actuators. The ability to directly andaccurately measure the giant flexoelectric effect for different types ofnon-calamitic liquid crystal molecules is important for identifyingmolecules that will be effective for particular applications.

While the invention has been described with reference to certainembodiments, it will be understood by those skilled in the art thatvarious changes may be made and equivalents may be substituted withoutdeparting from the scope of the invention. In addition, manymodifications may be made to adapt a particular situation or material tothe teachings of the invention without departing from its scope.Therefore, it is intended that the invention not be limited to theparticular embodiment disclosed, but that the invention will include allembodiments falling within the scope of the appended claims.

1. A method of creating an electro-mechanical energy conversion device,said method comprising: preparing a substance comprising at least onetype of liquid crystalline material with molecules having anon-calamitic shape; stabilizing said prepared substance to form amechanically flexible material; and applying at least one conductiveelectrode to said mechanically flexible material.
 2. The method of claim1 further comprising at least two conductive electrodes and connectingsaid at least two electrodes with an electrical device.
 3. The method ofclaim 2 wherein the electrical device is selected from the groupconsisting of a circuit, a resistive load, a current detector, a sourceof electrical potential difference or combinations thereof.
 4. Themethod of claim 1 wherein said stabilizing includes initiatingcross-linking between two or more functional groups of said at least onetype of liquid crystalline material with molecules having anon-calamitic shape to form a polymer matrix of covalent bonds.
 5. Themethod of claim 1 wherein said preparing includes dissolving compoundshaving reactive functional groups within said liquid crystallinematerial with molecules having a non-calamitic shape.
 6. The method ofclaim 5 wherein said stabilizing includes initiating cross-linkingbetween said reactive functional groups to form a polymer matrix.
 7. Themethod of claim 6 wherein said stabilizing includes initiatingcross-linking between said reactive functional groups to form a polymermatrix of covalent bonds or hydrogen bonds.
 8. The method of claim 1wherein said stabilizing includes initiating cross-linking between twoor more functional groups of said at least one type of non-calamiticliquid crystal molecules to form a polymer matrix of hydrogen bonds. 9.The method of claim 1 wherein said stabilizing includes capturing saidsubstance between elastic substrates.
 10. The method of claim 1 whereinsaid stabilizing includes capturing said substance within apre-established polymer mesh.
 11. The method of claim 1 furthercomprising aligning said non-calamitic shaped liquid crystal molecules,before stabilizing said substance, such that a direction of averagemolecular anisotropy in an undistorted state is substantially uniformacross the molecules.
 12. The method of claim 11 wherein said aligningis accomplished by at least one of surface treatment, mechanicaldeformation, external electric fields, and external magnetic fields. 13.The method of claim 1 wherein said non-calamitic shaped liquid crystalmolecules comprise bent-core liquid crystal molecules.
 14. The method ofclaim 1 wherein a liquid crystal phase of said non-calamitic liquidshaped crystal molecules is nematic.
 15. The method of claim 1 whereinsaid non-calamitic shaped liquid crystal molecules are capable ofexhibiting giant flexoelectricity.
 16. A method of creating anelectro-mechanical energy conversion device, said method comprising:preparing a substance comprising at least one type of liquid crystallinematerial with molecules having a non-calamitic shape and capable ofexhibiting a giant flexoelectric effect; stabilizing said preparedsubstance to form a mechanically flexible material; and applying atleast one conductive electrode to said mechanically flexible material.17. A method of creating an electro-mechanical energy conversion devicecomprising: preparing a substance comprising at least one type ofnon-calamitic liquid crystal molecules; stabilizing said preparedsubstance to form a mechanically flexible material, wherein themechanically flexible material comprises a polymer matrix; applying atleast one conductive electrode to said material, wherein mechanicalflexing of the mechanically flexible material generates electricalenergy which is received by the at least one electrode.
 18. The methodas in claim 17, wherein the polymer matrix is comprised of bondsselected from the group consisting of covalent bonds between two or morefunctional groups of reactive compounds dissolved in the non-calamiticliquid crystal molecules before the substance as stabilized, covalentbonds between two or more functional groups of the at least one type ofnon-calamitic liquid crystal molecules hydrogen bonds between two ormore functional groups of the at least one type of non-calamitic liquidcrystal molecules, hydrogen bonds between two or more functional groupsof reactive compounds dissolved in the non-calamitic liquid crystalmolecules before the substance is stabilized or combinations thereof.